Limits

Given the sequence

1a) Prove converges and then find the lim a.

b) If , give a value of that will guarantee that whenever . Then, verify this answer by picking an and checking

Hmm, okay so obviously the limit is .. but I know this from basic calculus (since we have the same power in the numerator/denominator). So would I proceed knowing this fact, and then proceeding with the convergence proof with .. that is:

Let be arbitrary. Then ____ ***have to find is a real number so there exists a natural number such that N > _____ ***same thing, have to find by the Archimedean Property. For this we have

OR, would I proceed to showing this converges by using the Monotone Convergence Thm (and thus pretty much making no assumptings as to what it converges to), and showing its bounded and monotone and therefore converges.

Thanks for the help Plato. I understand what you did, using the definition of convergence. But this doesn't show that it converges. I am assuming that (31/5)*|1/(5n^2 -3)| converges, and then using the |a_n - a| < epsilon to work out part b.